The class \([\Phi ]\in H^3(\mathsf {Out}(G),\mathbb {C}^{\times })\)  obtained from the associator of a morphism category of the topological defect bicategory \({B}_{\textsf {\tiny YM}}\)  is trivial, \([\Phi ]=1\) , so we can gauge any subgroup
\(\Gamma < \mathsf {Out}(G)\)  [1]}, which we now fix.
In order to compute the orbifold theory of two-dimensional Yang-Mills theory with defect
\(M=\bigoplus _{\varphi \in \Gamma }\,L_{\varphi }\) , we need to
give labels for junctions of the defect labeled with \(M\) .
It is enough to give the labels for trivalent junctions because, owing
to the fact that \(M\)  is a strongly separable symmetric Frobenius algebra
in \({B}_{\textsf {\tiny YM}}(L,L)\) , the value of the area-dependent quantum field theory
on a surface with a defect network is invariant under certain changes of
the defect network, which allow us to define junction fields with higher valency.
